Simplify the following expression: $p = \dfrac{5y^2 + 80y + 315}{y + 9} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ p =\dfrac{5(y^2 + 16y + 63)}{y + 9} $ Then we factor the remaining polynomial: $y^2 + {16}y + {63} $ ${9} + {7} = {16}$ ${9} \times {7} = {63}$ $ (y + {9}) (y + {7}) $ This gives us a factored expression: $\dfrac{5(y + {9}) (y + {7})}{y + 9}$ We can divide the numerator and denominator by $(y - 9)$ on condition that $y \neq -9$ Therefore $p = 5(y + 7); y \neq -9$